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Search: id:A122556
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| A122556 |
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Primes occur infinitely often, with first appearance in order. Between each occurance of a prime p, there are p distinct primes. |
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1
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| 2, 3, 5, 2, 7, 3, 2, 11, 13, 2, 3, 5, 2, 17, 3, 2, 19, 7, 2, 3, 5, 2, 23, 3, 2, 29, 31, 2, 3, 5, 2, 37, 3, 2, 7, 11, 2, 3, 5, 2, 41, 3, 2, 43, 13, 2, 3, 5, 2, 7, 3, 2, 47, 53, 2, 3, 5, 2, 59, 3, 2, 61, 7, 2, 3, 5, 2, 11, 3, 2, 17, 67, 2, 3, 5, 2, 71, 3, 2, 7, 19, 2, 3, 5, 2, 13, 3, 2, 73, 79, 2, 3, 5
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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From a suggestion by Eric Angelini. The primes between two occurrences of p always include all smaller primes, often more than once and p - PrimePi(p) + 1 larger primes, once each. (Here PrimePi is A000720, the number of primes <= n.)
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EXAMPLE
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Between the first and 2nd 5's, the sequence is 2,7,3,2,11,13,2,3; the distinct values are {2,3,7,11,13}, a set with 5 elements.
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CROSSREFS
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Cf. A001511, A000720.
Sequence in context: A138512 A066949 A073481 this_sequence A084346 A165911 A096062
Adjacent sequences: A122553 A122554 A122555 this_sequence A122557 A122558 A122559
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KEYWORD
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easy,nonn
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 20 2006
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